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Lesson8_card-1  Ka-fu Wong  ©  2007 ECON1003: Analysis of Economic Data Lesson 8, Additional Materials: Card demonstration of hypothesis  Card demonstration of hypothesis  tests tests

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Lesson8_card -2  Ka-fu Wong  ©  2007 ECON1003: Analysis of Economic Data Card experiment We are going to perform an experiment on a deck of 52 cards. Count the actual number of red cards out of 10 trials (with  replacement).  What is the probability of getting a red card on any trial? Hypothesis: p=0.5 Expected value = 0.5 Standard deviation = (0.5*0.5) 1/2  = 0.5
Lesson8_card -3  Ka-fu Wong  ©  2007 ECON1003: Analysis of Economic Data Card experiment results (10 trials) Trial Card color (B/R) Proportion (#Red/#trial) 1 B 0 2 B 0 3 B 0 4 B 0 5 B 0 6 B 0 7 B 0 8 B 0 9 B 0 10 B 0

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Lesson8_card -4  Ka-fu Wong  ©  2007 ECON1003: Analysis of Economic Data Hypothesis Hypothesis:  p = 0.5 Alternative Hypothesis: p < 0.5 Experiment results: # of red cards in 10 trials = x P(X=x) =C(10,x) p x (1-p) n-x = C(10,x) (0.5) x (0.5) 10-x X p(X) 0 0.00098 1 0.00977 2 0.04395 3 0.11719 4 0.20508 5 0.24609 6 0.20508 7 0.11719 8 0.04395 9 0.00977 10 0.00098 Is it possible for the deck of cards  to be a standard deck of cards (i.e.,  p=0.5)? Not very probable. Reject the original hypothesis
Lesson8_card -5  Ka-fu Wong  ©  2007 ECON1003: Analysis of Economic Data Hypothesis Hypothesis:  p=0.5 Alternative Hypothesis: p< 0.5 How many draws did it take before the class  started feeling uncomfortable with the  outcome? The probability that we do not get any red in  a sequence of x trials is   P(black) x  = 0.5 x X p(X) 1 0.5000  2 0.2500  3 0.1250  4 0.0625  5 0.0313  6 0.0156  7 0.0078  8 0.0039  9 0.0020  10 0.0010  Most of us were ready to reject the deck as fair  after 4 to 5 draws. (some would say 4, the  others would say 5) We had a good feel of how improbable the hypothesis was.

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